Theorem rbsyl 1521

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
rbsyl.1	|- (-. ps \/ ch)
rbsyl.2	|- (ph \/ ps)

Assertion

Ref	Expression
rbsyl	|- (ph \/ ch)

Proof of Theorem rbsyl

Step	Hyp	Ref	Expression
1		rbsyl.2	. 2 |- (ph \/ ps)
2		rbsyl.1	. . 3 |- (-. ps \/ ch)
3		rb-ax1 1517	. . 3 |- (-. (-. ps \/ ch) \/ (-. (ph \/ ps) \/ (ph \/ ch)))
4	2, 3	anmp 1516	. 2 |- (-. (ph \/ ps) \/ (ph \/ ch))
5	1, 4	anmp 1516	1 |- (ph \/ ch)

Syntax hints:  -. wn 3   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by:  rblem1  1522  rblem2  1523  rblem3  1524  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532